Pinning control of general complex dynamical networks with optimization

This paper addresses optimal pinning control of general complex dynamical networks. A pinning scheme with linear feedback is proposed to globally exponentially stabilize a network onto a homogeneous state. In particular, we answer an important and fundamental question about pinning control: how to select an optimal combination between the number of pinned nodes and the feedback control gain? Three illustrative examples are provided to show the effectiveness of the proposed technique.